Class 11 Physics Chapter 1 Notes : Conversion of Units Notes

Complete Notes on Conversion of Units

Complete Notes on Conversion of Units

Why Conversion of Units is Important

Unit conversion is a fundamental skill in physics for transforming measurements between systems (e.g., CGS to SI) or within a system (e.g., km/h to m/s), critical for solving numerical problems in CBSE, NEET, and JEE exams.

1. Definition

Unit conversion is the process of expressing a physical quantity in different units while preserving its dimensional consistency.

2. Key Conversion Factors and Formulas

Below are key conversion factors and formulas for common unit conversions, including units and dimensional formulae where applicable:

  • Length:
    • 1 km = 1000 m = 105 cm
    • 1 m = 100 cm = 102 cm
    • Dimension: [L]
  • Velocity:
    • 1 km/h = (1000 m / 3600 s) = 5/18 m/s
    • Formula: v (m/s) = v (km/h) × (5/18)
    • SI Unit: m/s
    • Dimension: [L][T]-1
  • Energy:
    • 1 erg = 1 dyne·cm = 10-5 g·cm2/s2 = 10-7 J
    • 1 J = 1 kg·m2/s2 = 107 erg
    • SI Unit: Joule (J)
    • Dimension: [M][L]2[T]-2
  • Force:
    • 1 dyne = 1 g·cm/s2 = 10-5 N
    • 1 N = 1 kg·m/s2 = 105 dyne
    • SI Unit: Newton (N)
    • Dimension: [M][L][T]-2
  • Pressure:
    • 1 dyne/cm2 = 10-1 Pa
    • 1 Pa = 1 N/m2 = 10 dyne/cm2
    • SI Unit: Pascal (Pa)
    • Dimension: [M][L]-1[T]-2

3. Real-Life Example

  • Car Speedometer: A car’s speed is displayed as 72 km/h, but engineers need it in m/s for calculations. Converting 72 km/h × (5/18) = 20 m/s ensures accurate analysis for safety features like braking distance.

4. Common Exam Questions and Answers

Q1. Convert 54 km/h to m/s.

Answer:

  • 1 km/h = (5/18) m/s
  • 54 km/h = 54 × (5/18) = (54 × 5) / 18 = 270 / 18 = 15 m/s
Q2. Convert 1 erg to joule and verify using dimensional analysis.

Answer:

  • 1 erg = 1 dyne·cm = 1 g·cm2/s2
  • In SI: 1 g = 10-3 kg, 1 cm = 10-2 m
  • 1 erg = (10-3 kg) × (10-2 m)2 / (s2) = 10-7 kg·m2/s2 = 10-7 J
  • Dimensional Check: Energy = [M][L]2[T]-2 in both CGS and SI, confirming consistency.
Q3. An acceleration is given as 2 cm/s2. Convert it to SI units.

Answer:

  • SI unit of acceleration: m/s2
  • 1 cm = 10-2 m
  • 2 cm/s2 = 2 × 10-2 m/s2 = 0.02 m/s2

5. Diagram/Table

The table below lists common unit conversions with their factors and dimensions, serving as a visual reference:

Quantity Conversion SI Unit Dimensional Formula
Length 1 cm = 10-2 m Meter (m) [L]
Velocity 1 km/h = (5/18) m/s m/s [L][T]-1
Force 1 dyne = 10-5 N Newton (N) [M][L][T]-2
Energy 1 erg = 10-7 J Joule (J) [M][L]2[T]-2
Pressure 1 dyne/cm2 = 10-1 Pa Pascal (Pa) [M][L]-1[T]-2

6. Quick Tips/Tricks

  • km/h to m/s: Multiply by 5/18 (1000/3600 = 5/18).
  • CGS to SI: Convert g to kg (×10-3), cm to m (×10-2), then adjust (e.g., 1 erg = 10-7 J).
  • NEET/JEE Trick: Use dimensional analysis to verify conversions (e.g., both erg and joule have [M][L]2[T]-2).
  • Memorization: “km/h to m/s: ×5, ÷18; erg to joule: ×10-7.”
  • Quick Check: Ensure units match the expected SI unit in the problem’s context.

Note: Unit conversion ensures consistency in calculations, making it essential for accurate problem-solving in physics.

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